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E60 / E61 (2004 - 2010) BMW 5-Series E60 Sedan was first seen in the Unites States in the fall of 2003 with a 2004 Model Year designation. The E61 wagon followed shortly there after. The E60/E61 5 series is now available as a 528i, 528xi, 535i, 535xi, 550i and a 535xi sports wagon! -- View the E60 Wiki

Yes I know about the HPFP, but it was replaced on this car before I bought it (CPO) last year. And I thought the HPFP issue was "fixed" by now. But who knows, maybe the pump they used is an older revision, I think it was replaced in late 2011.

I am thinking it could be the fuel injectors leaking fuel, while the car sits, or a bad LPFP/sensor, or even carbon build up on the intakes. The car has 46k miles on it and the spark plugs were just replaced at 40k (routine service). All 6 injectors were replaced about 10k miles ago as well.

If it is a leaking fuel injector usually the car would act flooded when you try to restart and should stumble a bit when it starts. To me it seems like the fuel pressure is bleeding off. the engine cranks until the fuel pressure comes up and then it starts and all seems well. Possibly a defective check valve in the fuel pump

2006 530i does not have HPFP, it has regular fuel pump.
As others suggested, fuel pressure regulator may not be holding the pressure. When was the fuel pump replaced? Did they replace the fuel filter as well at that time?

At 45K miles, with the fuel pump already replaced, now I am not sure if it is fuel pump issue.

my 2010 started just like this predominantly on cold starts like overnight. Dealer changed the HPFP and Low Pressure Fuel Sensor and it seems to have remedied the problem for now

Now my problem is misfiring, so I'll probably go back to get the injectors changed. I also realized today that usually when I start the car in the morning, it will start at an initial RPM then about a second or two later raise higher like its getting more power. So it might start at like 900 and raise up to 1200 or so a second or two later